Fully-heavy tetraquark spectra and production at hadron colliders

Motivated by the observation of exotic structure around 6900 MeV in the $J/\psi$-pair mass spectrum using proton-proton collision data by the LHCb collaboration, we study the spectra of fully-heavy tetraquarks within Bethe-Salpeter equation and Regge trajectory relation. The $X\left(6900\right)$ may be explained as a radially excited state with quark content $cc\overline{c}\overline{c}$ and spin-parity $0^{++}\left(3S\right)$ or $2^{++}\left(3S\right)$ or an orbitally excited 2P state. New $cc\overline{c}\overline{c}$ structures around 6.0 GeV, 6.5 GeV, and 7.1 GeV are predicted together. Other $bb\overline{b}\overline{b}$ and $bc\overline{b}\overline{c}$ structures which may be experimentally prominent are discussed. On the other hand, the fully-heavy S-wave tetraquark production at hadron colliders is investigated and their cross sections are obtained.